Semiparametric Regression with an Interval-Censored Covariate

In longitudinal studies, investigators are often interested in how the timing of an intermediateevent affects a future outcome. The intermediate event is often asymptomatic and its status can onlybe assessed at periodic examinations. Such an event is interval-censored in that its occurrence isonly known to lie in an interval induced by these examinations. The problem of interval-censoredcovariates has been previously studied only under restrictive conditions. In this dissertation, werelax these assumptions and present semiparametric regression models linking an interval-censoredintermediate event to various response variables.In the first chapter, we consider the case where the response variable of interest is continuous.We link the intermediate event and response through the rectified linear unit function, allowingfor interpretations in terms of duration of exposure to the intermediate event. We propose a nonparametricmaximum likelihood estimation approach using an expectation-maximization algorithm.We demonstrate the proposed approach through simulation studies and show that our method is robustto differential censoring patterns induced by missing visits. We present an application regressingsystolic blood pressure on interval-censored diabetes exposure.In the second chapter, we address the case where the response variable of interest is a rightcensoredevent time. We generalize the relationship between the outcome and intermediate event bylinking them through any non-constant function. We demonstrate the method through simulationstudies and a real data application.In the third chapter, we extend our previous work to longitudinal repeated measurements of acontinuous variable. We account for within-subject correlation through Gaussian-distributed randomeffects. We allow for time-dependent covariates to influence both the response and the occurrenceof the intermediate event. We demonstrate the approach through simulation studies and repeat theanalysis of Chapter 1 using repeated measurements of systolic blood pressure.In a brief fourth chapter, we develop regression models with an interval-censored covariate forresponse variables belonging to the exponential family. This extension provides researchers accessto analogs of generalized linear models such as logistic regression and the log-linear model. Wedemonstrate the performance of the approach, both with and without repeated measures, throughsimulation studies.Doctor of Philosoph